Large Fibonacci Numbers Part 1

It is given that the two large Fibonacci numbers:

\[ \begin{eqnarray} F_{100} &=& 354224848179261915075 \\ F_{110} &=& 43566776258854844738105 \\ \end{eqnarray} \]

What is the value of \(n\) such that the equation below is fulfilled?

\[ 1 + 2 + 3 + \ldots + n = \text{gcd} \left ( F_{100},F_{110} \right ) \]

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